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%I #21 Jul 08 2018 01:49:45
%S 3,7,31,211,2311,60653,1023053,19417793,446235509,12939711677,
%T 200560490131,14841484883609,608500576478849,26165522997357677,
%U 1229779567395958169,65178316970529225209,3845520700432469775917,234576762719782814756597,15716643102168462956621849
%N Smallest number m such that phi(m) is a multiple of n-th primorial number, the product of first n primes.
%H Ray Chandler, <a href="/A066676/b066676.txt">Table of n, a(n) for n = 1..25</a>
%F a(n) = Min{x : A000010(x) mod A002110(n) = 0}.
%e n = 8: a(8) = 19417793, phi(a(8)) = 19199380 = 2*9699690 = 2*2*3*5*7*11*13*17*19.
%t nmax = 25;
%t A066676 = {};
%t pm = 1;
%t Do[
%t pm *= Prime[n];
%t sol = 0;
%t If[PrimeQ[pm + 1],
%t sol = pm + 1;
%t ,
%t sd = Select[Divisors[pm/2], # <= Sqrt[pm/2] &];
%t Do[
%t f1 = sd[[i]];
%t f2 = pm/2/f1;
%t If[PrimeQ[2 f1 + 1] && PrimeQ[2 f2 + 1],
%t sol = (2 f1 + 1)*(2 f2 + 1);
%t Break[];
%t ];
%t , {i, Length[sd], 1, -1}];
%t ];
%t AppendTo[A066676, sol];
%t Print[{n, sol}];
%t , {n, nmax}];
%t A066676 (* _Ray Chandler_, Oct 21 2011 *)
%Y Cf. A000010, A002110, A066674, A066675, A066677, A066678.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 19 2001
%E a(9)-a(11) from _Donovan Johnson_, Oct 12 2011
%E a(12)-a(13) upper limits from _Donovan Johnson_ confirmed as next terms, a(14)-a(19) added by _Ray Chandler_, Oct 21 2011
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